Exceptional versus superPoincar\'e algebra as the defining symmetry of maximal supergravity

TL;DR

This paper explores how exceptional and superPoincaré algebras serve as the fundamental symmetries in constructing maximal supergravity, highlighting their interplay and implications for string and M-theory.

Contribution

It demonstrates the use of both symmetries in supergravity construction and reveals the necessity of non-trivial field redefinitions to relate them, impacting counterterm arguments.

Findings

Both symmetries can be used in supergravity construction.

In d=11, choosing one symmetry requires complex field redefinitions.

Full symmetry consideration is crucial for accurate counterterm analysis.

Abstract

We describe how one may use either the superPoincar\'e algebra or the exceptional algebra to construct maximal supergravity theories in the light-cone formalism. The d=4 construction shows both symmetries albeit in a non-linearly realized manner. In d=11, we find that we have to choose which of these two symmetries to use, in constructing the theory. In order to understand the other "unused" symmetry, one has to perform a highly non-trivial field redefinition. We argue that this shows that one cannot trust counterterm arguments that do not take the full symmetry of the theory into account. Finally we discuss possible consequences for Superstring theory and M-theory.